Clustering Under Prior Knowledge with Application to Image Segmentation
Mário A. T. Figueiredo, Dong Cheng, Vittorio Murino · The MIT Press eBooks · 2007
This paper proposes a new approach to model-based clustering under prior knowl-edge. The proposed formulation can be interpreted from two different angles: as penalized logistic regression, where the class labels are only indirectly observed (via the probability density of each class); as finite mixture learning under a group-ing prior. To estimate the parameters of the proposed model, we derive a (gener-alized) EM algorithm with a closed-form E-step, in contrast with other recent approaches to semi-supervised probabilistic clustering which require Gibbs sam-pling or suboptimal shortcuts. We show that our approach is ideally suited for image segmentation: it avoids the combinatorial nature Markov random field pri-ors, and opens the door to more sophisticated spatial priors (e.g., wavelet-based) in a simple and computationally efficient way. Finally, we extend our formulation to work in unsupervised, semi-supervised, or discriminative modes. 1